{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 02\n",
    "\n",
    "# 一元OLS线性回归\n",
    "Book_7《机器学习》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2a9c8552-4016-4078-8ac2-afd2de30a18a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# !pip install yfinance\n",
    "# 需要安装库，下载金融数据"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "793d7e20-a434-4334-bef3-9c92d872e9a6",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "685f712c-4639-4b55-8bf4-2e7518ef927a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import yfinance as yf\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a6654989-613c-4b46-8045-bd4fcc3510d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = plt.rcParams\n",
    "p[\"font.sans-serif\"] = [\"Roboto\"]\n",
    "p[\"font.weight\"] = \"light\"\n",
    "p[\"ytick.minor.visible\"] = False\n",
    "p[\"xtick.minor.visible\"] = False\n",
    "p[\"axes.grid\"] = True\n",
    "p[\"grid.color\"] = \"0.5\"\n",
    "p[\"grid.linewidth\"] = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4a6fee6-cd9c-4566-8882-3a20b4da6443",
   "metadata": {},
   "source": [
    "## 下载股价数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f1c896ee-5269-439c-8097-db48d515c8a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%%**********************]  2 of 2 completed\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">Adj Close</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Close</th>\n",
       "      <th colspan=\"2\" halign=\"left\">High</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Low</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Open</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-01-02</th>\n",
       "      <td>73.152664</td>\n",
       "      <td>3257.850098</td>\n",
       "      <td>75.087502</td>\n",
       "      <td>3257.850098</td>\n",
       "      <td>75.150002</td>\n",
       "      <td>3258.139893</td>\n",
       "      <td>73.797501</td>\n",
       "      <td>3235.530029</td>\n",
       "      <td>74.059998</td>\n",
       "      <td>3244.669922</td>\n",
       "      <td>135480400</td>\n",
       "      <td>3459930000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-03</th>\n",
       "      <td>72.441460</td>\n",
       "      <td>3234.850098</td>\n",
       "      <td>74.357498</td>\n",
       "      <td>3234.850098</td>\n",
       "      <td>75.144997</td>\n",
       "      <td>3246.149902</td>\n",
       "      <td>74.125000</td>\n",
       "      <td>3222.340088</td>\n",
       "      <td>74.287498</td>\n",
       "      <td>3226.360107</td>\n",
       "      <td>146322800</td>\n",
       "      <td>3484700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-06</th>\n",
       "      <td>73.018684</td>\n",
       "      <td>3246.280029</td>\n",
       "      <td>74.949997</td>\n",
       "      <td>3246.280029</td>\n",
       "      <td>74.989998</td>\n",
       "      <td>3246.840088</td>\n",
       "      <td>73.187500</td>\n",
       "      <td>3214.639893</td>\n",
       "      <td>73.447502</td>\n",
       "      <td>3217.550049</td>\n",
       "      <td>118387200</td>\n",
       "      <td>3702460000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-07</th>\n",
       "      <td>72.675262</td>\n",
       "      <td>3237.179932</td>\n",
       "      <td>74.597504</td>\n",
       "      <td>3237.179932</td>\n",
       "      <td>75.224998</td>\n",
       "      <td>3244.909912</td>\n",
       "      <td>74.370003</td>\n",
       "      <td>3232.429932</td>\n",
       "      <td>74.959999</td>\n",
       "      <td>3241.860107</td>\n",
       "      <td>108872000</td>\n",
       "      <td>3435910000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-08</th>\n",
       "      <td>73.844353</td>\n",
       "      <td>3253.050049</td>\n",
       "      <td>75.797501</td>\n",
       "      <td>3253.050049</td>\n",
       "      <td>76.110001</td>\n",
       "      <td>3267.070068</td>\n",
       "      <td>74.290001</td>\n",
       "      <td>3236.669922</td>\n",
       "      <td>74.290001</td>\n",
       "      <td>3238.590088</td>\n",
       "      <td>132079200</td>\n",
       "      <td>3726840000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Adj Close                   Close                    High  \\\n",
       "                 AAPL        ^GSPC       AAPL        ^GSPC       AAPL   \n",
       "Date                                                                    \n",
       "2020-01-02  73.152664  3257.850098  75.087502  3257.850098  75.150002   \n",
       "2020-01-03  72.441460  3234.850098  74.357498  3234.850098  75.144997   \n",
       "2020-01-06  73.018684  3246.280029  74.949997  3246.280029  74.989998   \n",
       "2020-01-07  72.675262  3237.179932  74.597504  3237.179932  75.224998   \n",
       "2020-01-08  73.844353  3253.050049  75.797501  3253.050049  76.110001   \n",
       "\n",
       "                               Low                    Open               \\\n",
       "                  ^GSPC       AAPL        ^GSPC       AAPL        ^GSPC   \n",
       "Date                                                                      \n",
       "2020-01-02  3258.139893  73.797501  3235.530029  74.059998  3244.669922   \n",
       "2020-01-03  3246.149902  74.125000  3222.340088  74.287498  3226.360107   \n",
       "2020-01-06  3246.840088  73.187500  3214.639893  73.447502  3217.550049   \n",
       "2020-01-07  3244.909912  74.370003  3232.429932  74.959999  3241.860107   \n",
       "2020-01-08  3267.070068  74.290001  3236.669922  74.290001  3238.590088   \n",
       "\n",
       "               Volume              \n",
       "                 AAPL       ^GSPC  \n",
       "Date                               \n",
       "2020-01-02  135480400  3459930000  \n",
       "2020-01-03  146322800  3484700000  \n",
       "2020-01-06  118387200  3702460000  \n",
       "2020-01-07  108872000  3435910000  \n",
       "2020-01-08  132079200  3726840000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_x_df_raw = yf.download(['AAPL','^GSPC'], start='2020-01-01', end='2020-12-31')\n",
    "y_x_df_raw.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f94216c2-ceda-4322-9a45-a57b0fb64fbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_x_df_raw.to_csv('y_x_df_raw.csv')\n",
    "y_x_df_raw.to_pickle('y_x_df_raw.pkl')\n",
    "# 如果不能下载，就用pandas.read_csv() 或 pandas.read_pickle() 读入\n",
    "# 建议使用 pandas.read_pickle() \n",
    "# y_x_df_raw = pd.read_csv('y_x_df_raw.csv')\n",
    "# y_x_df_raw = pd.read_pickle('y_x_df_raw.pkl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "125c98bb-52dd-4ea0-af6b-0cf03fa6b5c6",
   "metadata": {},
   "source": [
    "## 计算收益率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9c69165b-6861-487f-bbf4-05df0075098c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 收盘价，计算日回报率\n",
    "y_x_df = y_x_df_raw['Adj Close'].pct_change()\n",
    "y_x_df.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dae9aab3-2447-48d8-9485-57b4435ca117",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_x_df.rename(columns={\"^GSPC\": \"SP500\"},inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2a52db41-e7de-4d77-a9be-ac3a05926832",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>SP500</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-01-03</th>\n",
       "      <td>-0.009722</td>\n",
       "      <td>-0.007060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-06</th>\n",
       "      <td>0.007968</td>\n",
       "      <td>0.003533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-07</th>\n",
       "      <td>-0.004703</td>\n",
       "      <td>-0.002803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-08</th>\n",
       "      <td>0.016086</td>\n",
       "      <td>0.004902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-09</th>\n",
       "      <td>0.021241</td>\n",
       "      <td>0.006655</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL     SP500\n",
       "Date                          \n",
       "2020-01-03 -0.009722 -0.007060\n",
       "2020-01-06  0.007968  0.003533\n",
       "2020-01-07 -0.004703 -0.002803\n",
       "2020-01-08  0.016086  0.004902\n",
       "2020-01-09  0.021241  0.006655"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_x_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d9f8b33f-7f02-4acb-a2a9-a8d1d7de316d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_df = y_x_df[['SP500']]\n",
    "y_df = y_x_df[['AAPL']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93fac47c-1270-4c66-b01c-13c777623b82",
   "metadata": {},
   "source": [
    "## 数据分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bdc474f2-cec8-4602-8855-2bf4a519750d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x241b231ea40>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% Data analysis\n",
    "\n",
    "sns.jointplot(data=y_x_df, x=\"SP500\", y=\"AAPL\", kind = 'scatter',\n",
    "              xlim = [-0.15,0.15],ylim = [-0.15,0.15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6706a3e3-719b-4ba9-8107-4d08d79ea2eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x241b243fd60>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# marginal and joint KDE plots\n",
    "sns.jointplot(data=y_x_df, x=\"SP500\", y=\"AAPL\",\n",
    "              kind=\"kde\", cmap = 'Blues', fill = True,\n",
    "              xlim = [-0.15,0.15],ylim = [-0.15,0.15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d150d5-fd59-477b-959d-08129efcebf0",
   "metadata": {},
   "source": [
    "## 协方差矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "13fdf923-f182-48be-b03b-9116eea0d53c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02946919 0.02176789]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Vb568CADISY3HBfs1nLvcCwBIsppQkJmEv39hBwA8eOcE7D/RLN/Al96VgsZLPfD4+n7vbq+Id860B61f0cwUvPvpJVxz+wAAcdFRWPiTCfjrZ5fD9A3QSOg4ZkA1IX2ze/bswfr16/HEE0/goYcewjPPPIPCwkJUVlaqXb+Ip4+KkgMBAPjsnRpkLbpfsU/G/bPQ+MExRVrHlxcQb5sAAJiQlaG4mV9t/waxSQkAAIPJBM+1G3IgAABn/vwe7lz8AABgbOpExbEA8E3jeZhjY4LWN3Phffii5vgIr5IilUEnyIEAAPz9nB1zMhIU+9yVPhYnv+pWpF3suo5kqxkAMDnRIgcCAGDvcWPsGCMAwGjQ4YbHr3iSrznbgfunJ4VUP0GAHAgAgOOGF1F8OqXbUEi/apPJhKioKEXatGnT0NXVpUqlqI8+Kgpu5zVFmiRJ8Pv8irSEdBs6v2pRpLV92ogJWRkAAL/XG1C21+0BAIxLS4H9vHLgp6vXCYPZ1FcHQ2DjkcFkhOj3B6QDQLxtQkCrBVEwBr2AGx7l70iSAP+ANviJ8dFo7b6uSGu63Is7kiwAAF+QNnuvvy+4nRBnxsUBx15z+2AyfPenb6gW/7/UtwXWW8cp1KOFiw6pJ6RuAjbNjI7Y5AT02rsD0nUD/xgFmenh7OxGzLdP/8Hy+8uITU7AlYuXBs1v+qgW9/x8CT55owoAYEkYC7M1RtFa0S9uYjKutrH5lEIzzmLClWuegPSBM5eC3XqvXPdgrMU4aH5/GeNiTPjGEfhbvfkcsWYDFs9MgUEnQBCADxq+gfOm1oCbzZmSgK/tzkGuiNTGm7h6QgoGBltZkIsMqUtvMAR/Ag/xex9y/e1vyxjuHJ1fX0Rq3k+w+tX/Fx1fNmNC5hS8/k//V9AiMxfeh5Ovvx1S3Yj0OgH+IH9bQv2rohvi30F/jl4nwC8Ong8A9l43Pjz7DSSpb/8n7k3H/hPNihaHx2anYobNimb7New5eiHEGhJpR0jBQFNTE44dU/ZJS5KEc+fOBaTfd999w5bndrvhdisHCPkhQR/yn4HI4Pf5oAtlXu0gwZo8DmCIZaKHO0fmwvtwresq9jz3GwCAKcaC+RtW4a//8apiP0GnAySJS1JTyPyiBH0Ige1gvyjx29/aUL84vyhhuIfJms+/m3XjFyW8Xd+K+6cn4Ujjd91db568CJwEJo0bg6V3paDydPABh6QuLjqknpC+2eeffx42m02xTZo0Cb/85S8D0kNRVlaGuLg4xXYKjlu6kNtRb0cXYhLHDrtfsBtwbFICnJ1XBs1XnCNp3KD5Cek2nDtyQv7sdl5DfUU1MhfMVew348ECnP3r0WHrStSv+5ob8ZaoYfcL9vsdazHi6nXvoPnyOZxuuTshVE6XD2NMfc9JA3vkWruvB3bT0Q+GYwbUE9I3kp6eHtLm8wXvZxto06ZNcDgcii0Pcbd0Ibcjv9cLszVWkSYIAvQDBnN2t7QjeepkRdqkmTPwzRdfAeibMTBQ1LcDBLtb2pE87Q5Fnjk2Br5vBxj6PIGDD69fccAUY1GkWSckobcjcH440WB8fgkWk7JxUhD6Bhbe7LLDhbSEMYq06RNi0dzZ13dvNAT+GTNF6W46VvlbtZgM8Hzbd5AUa0JuanxAHfyiiBiTAYt+MiGg7P4piUS3k1sOj77++muUl5dj586duHQpcCBaMCaTCVarVbGxiyA4v9eruPHmLF2EcwOm7p0/WofMAdMNJ8yYiu6WvpHQlz5vQmreT+S8+JTxuNZ9FQDgc7thjhmj6Cq4u3ixvAaBwRgVcOOfufwhnD/2ifx5XJoNXRdaQTRSPr+EMcbvfnvzMpMDphGebr4SMN1wSnIMLl3tW8/iqw4nslKscl6S1QTHt60GHl/fIkX6m57mH7xzgrwGgb3XjcybjgWA+6cl4dSFK3C6fZg0bkzA7IFoI5fEHS1sGVDP93pR0ddff40PP/wQXq8XX3/9NcrKysJdL/pW3f5KzHv+afhcbuijDLja9g26mlsxec5dAIALH58GAHz5t4/xQOkaeG+4EB0Xi/qKarmMCx+fxqzHlyF9Vi4AQG/Q48iW1747x4EqLHhhLVy9TkSZTWj7xxfybIHa1/6M+9c9Dp+nr6XAGG3GhY/P4FrXFfn46Q/cixO731Tza6Db1Hv/uITiOWlw+/pWB7T3uHDp6g3cOamvpfCz1r7uw/oLV/DEvelw+/yIMRnw14bvZq181urAwzkTkW3rO0avE/BG7XdTbd//x2U8cW86rnt8MBp0+PKyU7G2wbFzdvx8Thq8fhGCAFy+6pIXPXqjtgU/z0+Dzy/B4xcRpRdw6NPQHnoo/IYcFE23RJBCHPHV3NyMmpoa+Hw+TJkyBQ888AB0Oh127dqFNWvW3HJFnhcm33IZRD9mtb/dMtpVIFLNqd8vVv0cHf/2f4StrOQX/7+wlXU7CKll4Mknn8Rjjz2GX/ziFwFrDnB6IRERkbaF1Oayc+dOREVFYdeuXXjjjTfgcHDkPxER/bA4ZkA9IbUMREdHY/ny5QCA69ev49ChQ+ju7kZMTAycTq7GRURE6uNNXD0jHkA4ZswYPProowAAp9OJQ4cOYefOnbBarXjooYcQF8cpgkRERFpyS2FWTEwMHnvsMWRnZ+PSpUvYvn17uOpFRESkIOh0YdtI6XtNLQSAjz/+GGfOnMFnn32GDRs24IUXXghnvYiIiBRCWp6dvpcRBQMnT57E6dOnIQgC8vPz8ctf/hK7du1CVlaWWvUjIiIilYUUDPzHf/wH4uPjMWvWLPzyl79U5HFqIRER/RA4gFA9IQUDs2bNwvnz53HmzBlYrVZMnjxZzuNb6oiI6IcwWsGA1+vF9u3bYTQaIYoi0tLSsHhx4CJLDQ0NqKmpQXR0NJxOJ4qLixUv8Nu/f788NV+v12PdunVynsPhQHl5OSwWCzweD/Ly8jB3bt8L4fbs2RPwpt/29nYUFBRg4cKFAICXXnoJ06dPV+yzbt26kB/YQwoG5s2bh3nz5kGSJBw5cgSHDx9GVFQU5s+fz5YBIiK6rR04cABr166FxdL3npbKykq0t7cjJSVF3keSJBw7dgylpaVy2rZt27B+/XoAwIkTJ5CVlYWZM2cCANra2lBVVYUlS5YAACoqKlBaWgr9t+Midu/ejby8PJjNZqxevTqgTq+99hoWLFggf87NzcWqVau+9zWOKMwSBAEPPPAA1q1bh1WrVuHLL79Ee3s79uzZg4sXL37vShAREQ1ntGYTeL1eORAAgKKiIhw+fFixz9GjR+Wn9H5Tp05Fa2vfS9waGxvlQAAAbDYb7Pa+F2a5XC5YLBY5EACAFStWoLq6GsH4/X7o9Xr5Ydzv98Ng+N7zAQDcwmwCnU6HRYsWYdGiRfD7/fjggw/w7rvvBowpICIiCofR6CbweDyIiYlRpOl0uoCbb3NzMwoKChRpubm5OHPmDCZNmoSoAa+eB/re4AsALS0tyMjIUORZrVa4XK6gdXr//ffx4IMPyp87OzuRmJgY+kUFcWuhxLf0ej0eeuihcBRFREQU1GgEAx0dHUhKSgpIF0VR8TnY+LnExET56T9Yfn8ZHR0dSE1NHfYcg9XJbrejvb0d5eXlEAQBCQkJWLp06RBXFSgswQAREZGWuN3ugEF5JpNJflrv5/P5FM33/UIZPC8IAvx+/6D5/WWM5BwXLlxQDOIHgPj4eGRmZiI/Px9AXyvF66+/jqeeemrYOvbjPA0iItKEcI4ZKCsrQ1xcnGIrKysLOKfBYBjyhi7XLchgekmS5Df9DjXYPtRzAMBHH32EefPmKdImTZokBwIAkJ6eDq/XG1J5ch1GtDcREdEoEXThW4Fw06b/Exs3blSkDWwVAIDk5GTU1tYOX7cgN3u73S735Q8VDCQnJ8NutyM9PX3Ic3i93qBjD4IZP348uru7MW7cuJD2Z8sAERFFHJPJBKvVqtiCBQNGoxE9PT2KNFEUA56809LS0NTUpEg7c+YMMjMzASCgSwKAPEAw2LE9PT0B9Tl06BAefvjhgHIqKioC0hwOB+Lj4wPSB8NggIiItEGnD982AlFRUejt7ZU/V1ZWKub4A0BBQUHAdMOzZ8/KT/vZ2dmor6+X89ra2uSndrPZDKfTCZ/PJ+dXVFSgqKhIUV5XV1fQJ/2MjAwcP35ckdbb2yt3UYSC3QRERKQNo/S2wccffxxbt26F2WyG1+uFzWbD5MmT5e6D/v76wsJCbN68GdHR0XA4HCguLpbLyM/Px759+1BXVwegb9Dghg0b5PySkhJs3rwZsbGxcLlcyMnJUaxt0NTUhGnTpgWtX15eHqqqqrB9+3bo9Xq4XC4sX758RNcoSD+S9YSfFyaPdhWIVFX72y2jXQUi1Zz6feDyvOF2/c1/C1tZYx57MWxl3Q7YMkBERJog8BXGqmEwQERE2hDG2QSkxAGEREREEY4tA0REpA1sGVANgwEiItKEkb5tkELHYICIiLSBLQOqYZhFREQU4dgyQERE2sCWAdUwGCAiIk3gmAH18JslIiKKcGwZICIibWA3gWoYDBARkTYwGFANuwmIiIgiHFsGiIhIE/iiIvUwGCAiIm3gbALV8JslIiKKcGwZICIibeAAQtUwGCAiIk0QGAyohsEAERFpA8cMqIbfLBERUYRjywAREWkCuwnUw2CAiIi0gcGAathNQEREFOHYMkBERNrAAYSqYTBARESawOWI1cMwi4iIKMKxZYCIiLSBAwhVw2CAiIi0gcGAahgMEBGRJggcQKgafrNEREQRji0DRESkDewmUA2DASIi0gaBjdlq4TdLREQU4dgyQERE2sCWAdUwGCAiIk2QGAyohsEAERHRELxeL7Zv3w6j0QhRFJGWlobFixcH7NfQ0ICamhpER0fD6XSiuLgYNptNzt+/fz8cDgcAQK/XY926dXKew+FAeXk5LBYLPB4P8vLyMHfuXADAnj174Ha7Fedqb29HQUEBFi5cCADYsWMHRFGEJEmIj49HSUnJiK6RwQAREWnDKLUMHDhwAGvXroXFYgEAVFZWor29HSkpKfI+kiTh2LFjKC0tldO2bduG9evXAwBOnDiBrKwszJw5EwDQ1taGqqoqLFmyBABQUVGB0tJS6L99/8Lu3buRl5cHs9mM1atXB9Tptddew4IFCwAABw8eRFFRESZOnAgAqK+vx8mTJzF79uyQr5FtLkREpA2CEL5tBLxerxwIAEBRUREOHz6s2Ofo0aPyU3q/qVOnorW1FQDQ2NgoBwIAYLPZYLfbAQAulwsWi0UOBABgxYoVqK6uDlofv98PvV4P4dvr6OrqkgMBALj77rvR0NAwomtkMEBERDQIj8eDmJgYRZpOp4PBoGxYb25uRkZGhiItNzcXjY2NAICoqKiAsk0mEwCgpaUl4Fir1QqXyxW0Tu+//z4efPBB+fNQZYeK3QRERKQNYVyO2O12B/TDm0ymgJtoR0cHkpKSAo4XRVHxWZKkgH0SExPlp/9g+f1ldHR0IDU1ddhzDFanocoOFVsGiIhIEyRBF7atrKwMcXFxiq2srCzgnD6fT9F8L9clyA14IEEQ4Pf7B7+eb8sYyTkuXLiAyZMnD3vuUOp3M7YMEBGRNoRxAOGmTZuwceNGRVqwpnWDwTDkDV2uWpBxCJIkQfdta0aw/JGeAwA++ugj/OIXvxj23CPFlgEiIoo4JpMJVqtVsQULBpKTk9HZ2TlsecFuyHa7HYmJiYPm33yO/u6EoXi93qDjAxgMEBFR5BB04dtCZDQa0dPTo0gTRRFer1eRlpaWhqamJkXamTNnkJmZCQAB4xMAyAMEgx3b09MTEJwcOnQIDz/8cEA5Q5UdKgYDRESkDaMQDAB9o/V7e3vlz5WVlfIc/34FBQUB0w3Pnj2L9PR0AEB2djbq6+vlvLa2NowbNw4AYDab4XQ64fP55PyKigoUFRUpyuvq6pKPuVliYiLa2trkz/X19ZgxY8aIrpFjBoiIiIbw+OOPY+vWrTCbzfB6vbDZbJg8eTJqa2sBAPn5+QCAwsJCbN68GdHR0XA4HCguLpbLyM/Px759+1BXVwegb9Dghg0b5PySkhJs3rwZsbGxcLlcyMnJUaxt0NTUhGnTpgWt37Jly/DKK69AkiSIogiLxRJ0oaKhCNJIhxyq5Hlh8mhXgUhVtb/dMtpVIFLNqd8HLs8bbt7L58NWVtSEjOF3iiBsGSAiIm3gi4pUw2+WiIgowrFlgIiItCEMU+goOAYDRESkDewmUA2/WSIiogjHlgEiItIEiS0DqmEwQERE2hDGtxaSEoMBIiLSBrYMqIbfLBERUYRjywAREWkDWwZUw2CAiIi0gcGAavjNEhERRTi2DBARkSZwaqF6GAwQEZE2MBhQDb9ZIiKiCMeWASIi0ga+qEg1DAaIiEgb2E2gGn6zREREEY4tA0REpAmcTaAeBgNERKQNDAZUI0iSJI12JQAg73fVo10FIlU1vPPGaFeBSDWeUztVP8cNlytsZUWbzWEr63bAMIuIiCjCsZuAiIg04cfRjn17YjBARESaIDIaUA27CYiIiCIcWwaIiEgT2C6gHgYDRESkCSKjAdWwm4CIiCjCsWWAiIg04UeyLM5ticEAERFpArsJ1MNuAiIiogjHlgEiItIENgyoh8EAERFpArsJ1MNggIiINIEDCNXDMQNEREQRji0DRESkCeIondfr9WL79u0wGo0QRRFpaWlYvHhxwH4NDQ2oqalBdHQ0nE4niouLYbPZ5Pz9+/fD4XAAAPR6PdatWyfnORwOlJeXw2KxwOPxIC8vD3PnzlWUf/z4cdTV1SE6OhorV67EuHHj5LyXXnoJ06dPV+y/bt06CIIQ0jUyGCAiIk0YrV6CAwcOYO3atbBYLACAyspKtLe3IyUl5aa6STh27BhKS0vltG3btmH9+vUAgBMnTiArKwszZ84EALS1taGqqgpLliwBAFRUVKC0tBR6vR4AsHv3buTl5cFsNgMA3nvvPXi9XrzwwgtB65ibm4tVq1Z972tkNwEREdEQvF6vHAgAQFFREQ4fPqzY5+jRo1i4cKEiberUqWhtbQUANDY2yoEAANhsNtjtdgCAy+WCxWKRAwEAWLFiBaqrqwEAHo8H586dkwOHgfx+PwyGW3u2ZzBARESaIErh20Ll8XgQExOjSNPpdAE33+bmZmRkZCjScnNz0djYCACIiooKKNtkMgEAWlpaAo61Wq1wuVwAgEOHDuHRRx8dtI6dnZ1ITEwM8YqCYzcBERFpQjhnE7jdbrjdbkWayWSSb9D9Ojo6kJSUFHC8KCpHMASrW2Jiovz0Hyy/v4yOjg6kpqYOmn/58mWYzWbs2bMHfr8fAPDEE0/IXQh2ux3t7e0oLy+HIAhISEjA0qVLg1/4INgyQEREEaesrAxxcXGKraysLGA/n8+naL7vF0pgIgiCfPMOpr+M4c5x5coVHD58GE8//TTWrl2LkpISvPzyy/J+8fHxyMzMxNq1a7FmzRrk5OTg9ddfH7Z+N2MwQEREmiCGcdu0aRMcDodi27RpU8A5DQbDkDf0fsFG7UuSBJ1ON2h+qOeIiopCSUmJXNaYMWOwaNEinD59GgAwadIk5Ofny/unp6fD6/UOW+ebMRggIiJNkKTwbSaTCVarVbEN7CIAgOTkZHR2dg5bt2A3e7vdLvflDxUMJCcny90Jg+UPlJmZifPnzw96zPjx49Hd3T1UlRUYDBAREQ3CaDSip6dHkSaKYsCTd1paGpqamhRpZ86cQWZmJgAEjE8AIA8QDHZsT0+PIjgZ2C3R2tqK8ePHA+ibljiQw+FAfHz8UJemwGCAiIg0QZSksG0jERUVhd7eXvlzZWUlFixYoNinoKAgYLrh2bNnkZ6eDgDIzs5GfX29nNfW1iYvGmQ2m+F0OuHz+eT8iooKFBUVAQAWLlyIt956S1H2wYMHce+99wIAMjIycPz4cUV+b2+v3K0QCkH6kSz2nPe76tGuApGqGt55Y7SrQKQaz6mdqp/jq87e4XcK0ZTE2JD39Xq92Lp1K8xmM7xeL2w2G5YvX47a2loAkPvrGxoa8MEHHyA6OhoOhwPFxcVyMAAA+/btk1sZfD4fNmzYIHcfOBwO7Ny5E7GxsXC5XMjJycH8+fPlY+vq6vDJJ59Ar9ejt7cXDz/8MLKzs+X8qqoqtLW1Qa/Xw+VyYfny5Zg0aVLI18hggOgHwmCAbmc/RDDwpT18wcDUpNCDgUjAbgIiIqIIx0WHiIhIE34c7di3JwYDRESkCSIYDaiF3QREREQRji0DRESkCewmUA+DASIi0oSRvG2QRobdBERERBGOLQNERKQJ7CZQD4MBIiLSBM4mUA+7CYiIiCIcWwaIiEgT2E2gHgYDRESkCSN92yCFjsEAERFpgl8c7RrcvjhmgIiIKMKxZYCIiDSB3QTqYTBARESa4GcwoBp2ExAREUU4tgwQEZEmsJtAPQwGiIhIEzibQD3sJiAiIopwbBkgIiJNYDeBehgMEBGRJnA2gXrYTUBERBTh2DJARESaILJhQDUMBoiISBP8jAZUw2CAiIg0gQMI1cMxA0RERBGOLQNERKQJfjYMqIbBABERaQK7CdTDbgIiIqIIx5YBIiLSBM4mUA+DASIi0gR2E6iH3QREREQRji0DRESkCZxNoB4GA0REpAnsJlAPgwEiIqIheL1ebN++HUajEaIoIi0tDYsXLw7Yr6GhATU1NYiOjobT6URxcTFsNpucv3//fjgcDgCAXq/HunXr5DyHw4Hy8nJYLBZ4PB7k5eVh7ty5ivKPHz+Ouro6REdHY+XKlRg3bpyct2PHDoiiCEmSEB8fj5KSkhFdI4MBIiLSBHGUZhMcOHAAa9euhcViAQBUVlaivb0dKSkp8j6SJOHYsWMoLS2V07Zt24b169cDAE6cOIGsrCzMnDkTANDW1oaqqiosWbIEAFBRUYHS0lLo9XoAwO7du5GXlwez2QwAeO+99+D1evHCCy8E1O/gwYMoKirCxIkTAQD19fU4efIkZs+eHfI1cgAhERFpgl8K3zYSXq9XDgQAoKioCIcPH1bsc/ToUSxcuFCRNnXqVLS2tgIAGhsb5UAAAGw2G+x2OwDA5XLBYrHIgQAArFixAtXV1QAAj8eDc+fOyYHDQF1dXXIgAAB33303GhoaRnSNDAaIiEgTREkK2xYqj8eDmJgYRZpOp4PBoGxYb25uRkZGhiItNzcXjY2NAICoqKiAsk0mEwCgpaUl4Fir1QqXywUAOHToEB599NFB6zhU2aFiNwEREUUct9sNt9utSDOZTAE30Y6ODiQlJQUcL4qi4rMUJMBITEyUn/6D5feX0dHRgdTU1EHzL1++DLPZjD179sDv9wMAnnjiCbkLYaiyQ8WWASIi0gS/JIVtKysrQ1xcnGIrKysLOKfP51M03/cLdgMeSBAE+eYdTH8Zw53jypUrOHz4MJ5++mmsXbsWJSUlePnll4c8dyj1uxlbBoiISBPCOYBw06ZN2LhxoyItWNO6wWAY8obeTxCEgDRJkqDT6QbND/UcUVFRitkBY8aMwaJFi3D69GncddddQ5YdKrYMEBFRxDGZTLBarYotWDCQnJyMzs7OYcsLdkO22+1ITEwcNP/mc/R3JwyWP1BmZibOnz8/bNmhYjBARESaMBqzCYxGI3p6ehRpoijC6/Uq0tLS0tDU1KRIO3PmDDIzMwEgYHwCAHmAYLBje3p6FMHJwGb/1tZWjB8/ftiyQ8VggIiINGE0ZhMAfc30vb298ufKykosWLBAsU9BQUHAdMOzZ88iPT0dAJCdnY36+no5r62tTV40yGw2w+l0wufzyfkVFRUoKioCACxcuBBvvfWWouyDBw/i3nvvBdA3ULGtrU3Oq6+vx4wZM0Z0jRwzQERENITHH38cW7duhdlshtfrhc1mw+TJk1FbWwsAyM/PBwAUFhZi8+bNiI6OhsPhQHFxsVxGfn4+9u3bh7q6OgB9gwY3bNgg55eUlGDz5s2IjY2Fy+VCTk6OvLbBxIkTkZaWhm3btkGv16O3txePPPKIPL1x2bJleOWVVyBJEkRRhMViwerVq0d0jYI00iGHKsn7XfVoV4FIVQ3vvDHaVSBSjefUTtXP8cfjX4etrNK5d4StrNsBWwaIiEgT/KO0HHEk4JgBIiKiCDfiloHjx4+jubkZkiTJoxsFQUBqaioKCgrCXkEiIiKALQNqCjkYOHv2LI4ePYoFCxYEvFYRAJqamvDHP/4R8+bNQ25ublgrSURExGBAPSEHAx988AH++Z//edD8adOmYdq0adi8eTODASIiCjsGA+oJecxAdHR0SPvd/JpHIiIi+vELuWXg2rVrIe1388IMRERE4cKWAfWEHAysXLkS27dvx/Tp05GTk4OEhAQ5r7u7G6dPn0ZTU5NikQUiIqJwYTCgnpCDAZvNhl/96le4ePEi6uvr0dnZCVEUodPpkJSUhKysLCxcuFDNuhIREZEKRjy1MDU1FampqWrUhYiIaFBsGVDPiIKBuro6NDQ0wGw2QxRFxVuUXC4XZsyYEXTaIRER0a1iMKCekIOBiooKTJ06FWvWrBl0n1OnTmHv3r14+umnw1I5IiIiUl/IwcCVK1dw1113DblPXl4ePv7441utE93EoBOwcnYqvH4ROkHAZccNHD3XGbDflOQYzJ4yDm6viGijHn9tuAx7z3fvuP5pzgTEmKMAAKIo4c+ftMp5MSYDlt1tg8vrh0GvwxftPfj04lU5/9FZkwLOV3/hCpo7r0GvE7DinkkQBMDnl6DXCXir7iIYwFMoDAY9nls5Hx6vDzqdgIuXu3Ho6D8C9suekoL5s7Nww+1FTLQJ//3XOrTbr8r5P//pbFhjxgAA/KKI8j//Tc6zxkTjF8vuxzWXG0aDAae/aEHtp+eD1ueFpx7CJ59fwLHTTUibmIBF92YH7JOfk4Hn/+/yW7tw+l7YMqCekIMBnS60JQn0ev33rgwFeihnIv5S3waX1w8AKMxMQlKsCfZet2K/mWnx2H+iRf782OxUvHnyIgAgJzUeF+zXcO5y37TPJKsJBZlJ+PsXdgDAg3dOwP4TzfINfOldKWi81AOPTwQAuL0i3jnTHrR+RTNT8O6nl3DN3fce7rjoKCz8yQT89bPLYfoG6Hb284dmY/df/o7rLg8AoKhwJiYmxePSTTd6ALh35lRs2f+B/Pm5x+bj1TePAADm5EzBFxcu49Nzfb/3lKR4LC7IRfXfPwUArHxwFv5r/2GI3/7AVy29D6cbm+H2+BTn+EmGDVd7r8ufWy514U9v/Q0DuVzeW7xq+r4YDKgn5EWHBEHAN998M+Q+7e3Bbxj0/Rl0ghwIAMDfz9kxJyNBsc9d6WNx8qtuRdrFrutItpoBAJMTLXIgAAD2HjfGjjECAIwGHW54/Ion+ZqzHbh/elJI9RMEyIEAADhueBGl5/uvKDQGg14OBACg+u+fYuGcGYp97rtrGj48eVaRdv5iB2zJYwEAmZMnyoEAALTbryJxbCwAwGQ04PoNtxwIAMDbNfV45H7lKqmCIGDerEx8VNc4ZH0XzJmBD4fZh0iLQm4ZePbZZ1FZWYnu7m5ERUUpBg8KggC3242kpCQ899xzqlQ0Ehn0Am54/Io0SQqMjifGR+N08xVFWtPlXkyfGIuOHhd8QaJpr7/vqX9CnBkXu68r8q65fTAZvruhDxWL/6W+LbDeOmGII4j6RBn0uHbDpUiTJAm+b3+b/dInJuDY6SZF2j+aWpE7PRVtHVfg8yn/jQCAx9sXoKZNSMD5ix2KvN5rLphNUYq0xx+egzffr0P0gPSBbMljUfPx2SH3IfUE+1tG4TGi2QRLly5Vqx4UxDiLCVeueQLSBUF5sw12671y3YOxFuOg+f1ljIsx4RvHjSHPEWs2YPHMFBh0AgQB+KDhGzjdvoBjAGDOlAR8bXcOckVE30keZ4X9SuCKpbqBv+8gP+DOK71I+vbpP1h+fxlJ46xo/aZ70Hygr1vBL4ro6O5B+sSEgH37TUyKR1vHlUHzSX3sJlBPyMFAU1MTpk2bpkjz+/1455134HQ6YTAYUFhYiAkTJoS9kpFKrxPglwJ//KE+dw/8oxqsDL1OwIAHsYBz2Hvd+PDsN5Ckvv2fuDcd+080K6L0x2anYobNimb7New5eiHEGlIkM+h18PuD/L5D/IHrh2iB6i+j7xyBP/Cbz1HySD7+c8+hYc+3YHYW/nd1bWiVI1UwGFBPyMHA3/72N0Uw0NPTgz/96U945plnYLVaIUkS3n33XRgMBjz00ENDluV2u+F2KwfAiT4vdIahm+gijV+UoA/hL+Ng/zzEbwOJof75+EUJw3Xx13z+3VgRvyjh7fpW3D89CUcav2t+ffPkReAkMGncGCy9KwWVpzl+hIbm84vQ60P4fQ/yA+4fBzBY/nfnGPwHvrggF+8Fmb0wkE4nQJKg6B4lup2EPNJr4D+Ct956C6WlpbBarQD6mpUXL16MlpaWYIcrlJWVIS4uTrF9c2z/CKt+++u+5ka8ZfgAKdgfqLEWI65e9w6aL5/D6Za7E0LldPkwxtQXRw58OGvtvg4dxwxQCDq6e5AYHzvsfsF+v0ljY9F51Tlofj97d488mDCYvBnpuOcnd2D1svuxetn9WPngLDxyfw6eeCRfsd+i/Gwcrv182LqSuvySFLaNlEJuGQjopxaEoNMIQ5mCuGnTJmzcuFGRVvj7D0OtSsTw+SVYTMr/RYLQN7DwZpcdLqQljEFL13cDAadPiEVzZ98fS6Mh8P+JKUonH7vQNh6ft/XIeRaTAZ5vm1aTYk2YGB+tWHdAEPrmcseYDJg7LRHvD5hG2D8lkWgoXp8fsRblq9EFQYDBoPzNt1zuxtS0ZHzZ8l1LVO70VJxr7vvdGY2BAbPp24GALZe7sGLhPaj//IKcF2sxy9MK/59XDiqOS5+YANv4cQEDFickxuH94w0jvEIKN3YTqOd7zwGLigr+xDqw+T8Yk8kEq9Wq2NhFEJzPL2GM8buga15mcsA0wtPNVwKmG05JjsGlq30jtb/qcCIrxSrnJVlNcHzbauDx9S1SdHP/64N3TpDXILD3upF507EAcP+0JJy6cAVOtw+Txo0JmD0QbeRaExQan8+HmDFm+fOSeTNxZMA0wmOnm7BgjnLxn6wpKWi51AUAOPtVO+7KSpPzUpLiccXR98p1t8cHS7RJ0VWw8sFZ8hoEoUibmIAL7YELfRHdTkJuGZAkCa+//rr8+erVq3j77bexfPlyAMCJEydw+vRpPPLII+GvZQR77x+XUDwnDW5f3+qA9h4XLl29gTsnxQEAPmt1AOhbEfCJe9Ph9vkRYzLgrw3fPa1/1urAwzkTkW3rO0avE/BG7XfdOe//4zKeuDcd1z0+GA06fHnZqVjb4Ng5O34+Jw1evwhBAC5fdcmLHr1R24Kf56fB55fg8YuI0gs49Okl1b8Xuj0ceO8kflX8AFxuL6IMerTbr6D5Uhdm3zkFAHDys68AAEfrz+GfnliEG24P4mLG4L//WieXcfKzr1Dy8Bzck30HgL5Bg9veqJHzK94/iX9+YhF6r7tgNkbhsy9bFWsbDGf+rEzsOXgsHJdLt4gtA+oRpDCNiLl06RImTpz4vY/P+111OKpB9KPV8M4bo10FItV4Tu1U/RxrX68PW1nlT90dtrJuB2FbKu5WAgEiIiIaPSNadOijjz5CS0sLBEGAx+NBQUFBwNoDREREavCLHJyslpCDgT//+c9IT0/HqlWr5LSdO3dCEARMnTpVlcoRERH145gB9YTcTWC325GXl6dIe/bZZ3HkyJGwV4qIiIh+OCG3DAyc+ztcOhERUTixZUA9I5paGMzAxYiIiIjUwLcWqoeP9UREpAlsGVBPyMGA2+1WLDoE9LUWXL9+PSD9qaeeCk/tiIiISHUhBwMbNmxAR0cHqqursWLFCsTF9a1md+3aNVRVVeHGjRu44447MG/ePNUqS0REkYstA+oJORior69HXV0dnnvuOfllRD6fDy+//DJefPFF6HQ61NbW4uDBg1i2bJlqFSYiosjEYEA9IU8t/Oijj/CrX/1K8VbCiooKPPvss3Jafn5+SK8wJiIioh+PkFsGoqOjA9KuXLmCxMRERdpgbzMkIiK6FaPVMuD1erF9+3YYjUaIooi0tDQsXrw4YL+GhgbU1NQgOjoaTqcTxcXFsNlscv7+/fvhcPS9XE6v12PdunVynsPhQHl5OSwWCzweD/Ly8jB37lw5/9VXXw04X2FhITIzMwEAL730EqZPn67IX7duXcgz/kIOBoxGo+Lz5cuXg76PwO/3B6QRERHdqtEKBg4cOIC1a9fCYrEAACorK9He3o6UlBR5H0mScOzYMZSWlspp27Ztw/r16wH0vdk3KysLM2fOBAC0tbWhqqoKS5YsAdDX0l5aWgq9vu8V8Lt370ZeXh7M5r5XfJvNZsUKwAPl5uYOmT+ckLsJrl27BvGmdaFff/11LF26NOh+REREtwuv1ysHAgBQVFSEw4cPK/Y5evQoFi5cqEibOnUqWltbAQCNjY1yIAAANpsNdrsdAOByuWCxWORAAABWrFiB6urQ3ubr9/tveQHAkI9evXo1Xn75ZYwdOxadnZ2YP3++4uTNzc147bXXbikyISIiGow0Ci0DHo8HMTExijSdThdw821ubkZBQYEiLTc3F2fOnMGkSZOCdqGbTCYAQEtLCzIyMhR5VqsVLpdL/jxUc39nZ2dAl/1IhRwMxMXF4YUXXgia19vbi88//xy//vWv5SYNIiKicBLDGAy43W643W5Fmslkkm/Q/To6OpCUlBSkLso3KAZbpTcxMVF++g+W319GR0cHUlNThzzH1atXsXfvXvh8PoiiiJUrV8pT/O12O9rb21FeXg5BEJCQkBC05X4oIXcTDCU2NhaLFy9mIEBERJpQVlaGuLg4xVZWVhawn8/nUzTf9xtsif6bCYIw5Di6/jJCOUdKSgqefPJJrFmzBqtXr8bOnTvh9XoBAPHx8cjMzMTatWuxZs0a5OTkBCwGOJywBANERERqkyQpbNumTZvgcDgU26ZNmwLOaTAYQhoYH6wZX5Ikeer9UM38oZzj0UcflcsyGAx45pln5DEFkyZNQn5+vrxvenq6HCiEisEAERFpgiRKYdtMJhOsVqtiG9hFAADJycno7Owctm7BbvZ2u13uyx8qGEhOTpa7E0IVHx+P3t7eQfPHjx+P7u7ukMtjMEBERJogilLYtlAZjUb09PQMqIcY8OSdlpaGpqYmRdqZM2fkdQAGjk8AIA8QDHZsT0+PHJy0t7fj+PHjAXXoH8RYUVERULbD4UB8fPxwlydjMEBERDSEqKgoxVN4ZWUlFixYoNinoKAgYLrh2bNnkZ6eDgDIzs5GfX29nNfW1oZx48YB6FtDwOl0wufzyfkVFRUoKioC0Dde4NSpU4qy3333XRQWFgIAMjIyAoKF3t5exYrBw+ErjImISBMkcfh91PD4449j69atMJvN8Hq9sNlsmDx5MmprawFA7q8vLCzE5s2bER0dDYfDgeLiYrmM/Px87Nu3D3V1dQD6Bg1u2LBBzi8pKcHmzZsRGxsLl8uFnJwcxdoGjzzyCLZs2aJYBbF/0aO8vDxUVVVh+/bt0Ov1cLlcWL58+YiuUZBCGRL5A8j7XWiLKxBpVcM7b4x2FYhU4zm1U/Vz3P+/PghbWUf/x8Lhd4og7CYgIiKKcOwmICIiTQjnokOkxGCAiIg0YTSWI44U7CYgIiKKcGwZICIiTWDLgHoYDBARkSaIP47Jb7cldhMQERFFOLYMEBGRJrCbQD0MBoiISBMYDKiHwQAREWkC1xlQD8cMEBERRTi2DBARkSb8SF6lc1tiMEBERJowWm8tjATsJiAiIopwbBkgIiJN4ABC9TAYICIiTeDUQvWwm4CIiCjCsWWAiIg0gS0D6mEwQEREmsAXFamH3QREREQRji0DRESkCewmUA+DASIi0gQGA+phMEBERJrAdQbUwzEDREREEY4tA0REpAl8UZF6GAwQEZEmcMyAethNQEREFOHYMkBERJrAAYTqYTBARESaIIn+0a7CbYvdBERERBGOLQNERKQJbBlQD4MBIiLSBAYD6mE3ARERUYRjywAREWmC5GfLgFoYDBARkSawm0A9DAaIiEgTRisY8Hq92L59O4xGI0RRRFpaGhYvXhywX0NDA2pqahAdHQ2n04ni4mLYbDY5f//+/XA4HAAAvV6PdevWyXkOhwPl5eWwWCzweDzIy8vD3Llz5fxXX3014HyFhYXIzMwEAOzYsQOiKEKSJMTHx6OkpGRE18hggIiIaAgHDhzA2rVrYbFYAACVlZVob29HSkqKvI8kSTh27BhKS0vltG3btmH9+vUAgBMnTiArKwszZ84EALS1taGqqgpLliwBAFRUVKC0tBR6vR4AsHv3buTl5cFsNgMAzGYzVq1aFbR+Bw8eRFFRESZOnAgAqK+vx8mTJzF79uyQr5EDCImISBMk0R+2bSS8Xq8cCABAUVERDh8+rNjn6NGjWLhwoSJt6tSpaG1tBQA0NjbKgQAA2Gw22O12AIDL5YLFYpEDAQBYsWIFqqurQ6pfV1eXHAgAwN13342GhoYQr64PgwEiItKE0QgGPB4PYmJiFGk6nQ4Gg7Jhvbm5GRkZGYq03NxcNDY2AgCioqICyjaZTACAlpaWgGOtVitcLpf8WRCEQes4VNmhYjcBERFFHLfbDbfbrUgzmUwBN9GOjg4kJSUFHC+KouJzsNcrJyYmyk//wfL7y+jo6EBqauqQ57h69Sr27t0Ln88HURSxcuVKxMXFDVt2qNgyQEREmhDOloGysjLExcUptrKysoBz+nw+RfO9XJcgN+CBBEGAf4jpkP1lhHKOlJQUPPnkk1izZg1Wr16NnTt3wuv1Dlt2qNgyQEREmiCGcTbBpk2bsHHjRkVasKZ1g8Ew5A29X7BmfEmSoNPpBs0fyTkeffRRxf7PPPMMqqur8bOf/WzIskPFlgEiIoo4JpMJVqtVsQULBpKTk9HZ2TlsecFuyHa7HYmJiYPm33yO/u6EUMXHx6O3t3fYskPFYICIiDRhNAYQGo1G9PT0KNJEUQxook9LS0NTU5Mi7cyZM/I6AAPHJwCQBwgGO7anp0cOTtrb23H8+PGAOvQPYhyq7FAxGCAiIk0YramFUVFR8lM40LfOwIIFCxT7FBQUBEw3PHv2LNLT0wEA2dnZqK+vl/Pa2towbtw4AH1rCDidTvh8Pjm/oqICRUVFAPrGC5w6dUpR9rvvvovCwkIAfQMV29ra5Lz6+nrMmDFjRNfIMQNERERDePzxx7F161aYzWZ4vV7YbDZMnjwZtbW1AID8/HwAfSsCbt68GdHR0XA4HCguLpbLyM/Px759+1BXVwegb9Dghg0b5PySkhJs3rwZsbGxcLlcyMnJUaxt8Mgjj2DLli2KVRD7Fz1atmwZXnnlFUiSBFEUYbFYsHr16hFdoyCNdMihSvJ+F9riCkRa1fDOG6NdBSLVeE7tVP0cCUW/D1tZXe/8Lmxl3Q7YMkBERJrAFxWph8EAERFpAoMB9XAAIRERUYRjywAREWkCWwbUw2CAiIg0QRrhevsUOnYTEBERRTi2DBARkSawm0A9DAaIiEgTGAyoh90EREREEY4tA0REpAnhfIUxKTEYICIiTZD8DAbUwm4CIiKiCMeWASIi0gQOIFQPgwEiItIEBgPqYTBARESawGBAPRwzQEREFOHYMkBERJrAlgH1CJIkSaNdCfphud1ulJWVYdOmTTCZTKNdHaKw42+caGQYDESgnp4exMXFweFwwGq1jnZ1iMKOv3GikeGYASIiogjHYICIiCjCMRggIiKKcAwGIpDJZML//J//kwOr6LbF3zjRyHAAIRERUYRjywAREVGEYzBAREQU4RgMEBERRTguR3wbOHLkCOrq6vDrX/86IO/69et49tlnsW/fPkX6hQsXsHXrVkydOhWCIECSJLhcLvziF7+QF2l57bXXsGrVqh/kGoj6Xb16FXv27MGYMWPg9Xpx/fp1zJs3D7NmzcJ//dd/wWg0AgAEQYDf70diYiJWrlwpH//qq68GlFlYWIjMzEwAwI4dOyCKIiRJQnx8PEpKSuT9Wltb8d///d8YM2YMbty4gUWLFiE7O1vlKyYafQwGbgPnz59HXFxc0Lz33nsPK1euxIULFzB58mRF3tKlS1FQUCB/9ng82LZtG1544QU1q0s0pN27d+Of/umfYDB89+dp69atSE1NhdVqDQhQP/nkExw5cgTz588HAJjN5kGD2IMHD6KoqAgTJ04EANTX1+PkyZOYPXs2AKCqqgr/8i//Iu+/fft2BgMUEdhNoHGiKEKv12PWrFn4+OOPA/K7urqwcuVK1NTUDFuW0WhEQkIC/H6+DIRGT3x8vCIQAIDnnnsO1dXVQfe/55570NLSElLZXV1dciAAAHfffTcaGhoAAC0tLZg2bZpi/wULFuDYsWMjqT6RJjEY0LgjR46gsLAQd911F06fPq3Iu3btGmJiYmAwGOD1ekMqLzExEV1dXSrUlCg0nZ2dAWkGgwErVqwY9BhBEIL+90BRUVEBaf1rETQ2NiInJ0eRN23aNDQ3Nw9XZSLNYzCgcefPn8eUKVOC5h06dAg//elPAQBTpkzBV199NWx5ra2tSEpKCmsdiUZi3rx5+Ld/+ze0t7cr0uPj4wc9xu12y/999epV7N27F7t27cKf/vQnOBwOOS/YsiqiKALoC0ISExMHzSe6nXHMgIb5/X5Fc2p+fj5qa2uRn58PoK9JdOzYsQD6mjt37do1aOAAAOfOnYMoikM+WRGpbdasWcjNzUVVVRUuXbqE+Ph4/PznPw/6VA/0DQi8eexLSkoKli9fDp1OB5/Ph82bN6O0tHTQ4/sDhMF++1yXjSIBgwENq6mpkQdNAcDMmTOxfft25Ofno7e3F7GxsXKeXq8P6Cqorq7Gl19+CaDvD15CQgKee+65H6byREMwGo149NFHAQB2ux3//u//jtLSUvT29qK8vFzez+v1Yv78+Zg+fbqc1n8c0Ne98Mwzz6C6uho/+9nPhgx0dTodJEliMEwRicGAhp08eRKtra04cuSInPaPf/wDkiTh0KFD6OzsVPzh/Oqrr3D+/HlkZGQAABYvXqx4oiIabT09PfLU1n5JSUl48cUX8eabbyI2NnbE013j4+PR29sLYOjxBP3jZQZ2FTA4oEjAYECjfD4fUlJSsGbNGkX6nDlzcOLECVy9ehWlpaWKPFEUsWvXLjkYIPqx+fvf/47s7OyAabAGgwE3btwImGUwUHt7O5qbmzF37lw5TRRF+bibxxb0c7lcAIAZM2bgzJkzWLRokZx37tw5pKamft/LIdIMDiDUqA8++AAPPPBAQHp2djZOnjwZ8HQF9DWDctog/ZgtWLAAe/bsCUg/ceJEQIAQTEpKCk6dOqVIe/fdd1FYWAig7+m/ra1Nzquvr8eMGTMAAKmpqTh37pzi2EOHDsnHEt3O2DKgUV9//bU8U2CgGzdu4KGHHgqaN336dDQ1NQ06mOpmX3zxRcBqbnfccYfiyYkonKKjo7Fq1Sr867/+K8aMGQODwQCPx4O0tDQsX74cr7322rBlPPLII9iyZQuMRiNEUURaWhpSUlIAAMuWLcMrr7wCSZIgiiIsFgtWr14tH7ts2TL853/+J2JiYnDt2jXMnz+f3QQUEfgKYyIiogjHbgIiIqIIx2CAiIgowjEYICIiinAMBoiIiCIcgwEiIqIIx2CAiIgowjEYICIiinAMBoiIiCIcgwEiIqIIx2CAiIgowjEYICIiinAMBoiIiCLc/w/O1zuZS/5kMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SIGMA = y_x_df.cov()\n",
    "\n",
    "fig, axs = plt.subplots()\n",
    "\n",
    "h = sns.heatmap(SIGMA, annot=True,cmap='RdBu_r')\n",
    "h.set_aspect(\"equal\")\n",
    "print(np.sqrt(np.diag(SIGMA)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01128bb7-83c7-4b3b-a3df-ed96b131c1cb",
   "metadata": {},
   "source": [
    "## 相关系系数矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ab3594ce-c78d-4dec-9851-825d6eb009a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "RHO = y_x_df.corr()\n",
    "\n",
    "fig, axs = plt.subplots()\n",
    "\n",
    "h = sns.heatmap(RHO, annot=True,cmap='RdBu_r')\n",
    "h.set_aspect(\"equal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4539656-7d9c-4b7e-aa59-96683a58ddac",
   "metadata": {},
   "source": [
    "## 相关系转换为角度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7adb1052-d916-42cc-9a2e-fe30d6bf5f8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Angles = np.arccos(RHO)*180/np.pi\n",
    "fig, axs = plt.subplots()\n",
    "\n",
    "h = sns.heatmap(Angles, annot=True,cmap='RdBu_r')\n",
    "h.set_aspect(\"equal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91794808-a65b-45c0-a149-a1e4650d0e6b",
   "metadata": {},
   "source": [
    "## 向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4461b3eb-987e-415e-82f3-cf16d19e11e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_vector(vector,RBG): \n",
    "    array = np.array([[0, 0, vector[0], vector[1]]])\n",
    "    X, Y, U, V = zip(*array)\n",
    "    plt.quiver(X, Y, U, V,angles='xy', scale_units='xy',scale=1,color = RBG)\n",
    "\n",
    "angle = Angles['AAPL']['SP500']*np.pi/180\n",
    "\n",
    "vols = np.sqrt(np.diag(SIGMA))\n",
    "v_1_x = vols[1]\n",
    "v_1_y = 0\n",
    "\n",
    "v_2_x = vols[0]*np.cos(angle)\n",
    "v_2_y = vols[0]*np.sin(angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b301cba5-89d8-4182-8a64-ff37595601e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "draw_vector([v_1_x,v_1_y],np.array([0,112,192])/255)\n",
    "draw_vector([v_2_x,v_2_y],np.array([255,0,0])/255)\n",
    "plt.ylabel('$y, TSLA$')\n",
    "plt.xlabel('$x, S&P500$')\n",
    "plt.axis('scaled')\n",
    "plt.axhline(y=0, color='k')\n",
    "plt.axvline(x=0, color='k')\n",
    "ax.set_xlim([-0.01, 0.03])\n",
    "ax.set_ylim([-0.01, 0.03])\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1d45c01-7267-45c2-b9fc-24863c7126b7",
   "metadata": {},
   "source": [
    "## OLS线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80805657-6e0b-4288-97de-357cb51add66",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   AAPL   R-squared:                       0.689\n",
      "Model:                            OLS   Adj. R-squared:                  0.687\n",
      "Method:                 Least Squares   F-statistic:                     550.5\n",
      "Date:                Thu, 23 Nov 2023   Prob (F-statistic):           5.16e-65\n",
      "Time:                        11:09:43   Log-Likelihood:                 675.37\n",
      "No. Observations:                 251   AIC:                            -1347.\n",
      "Df Residuals:                     249   BIC:                            -1340.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0019      0.001      1.819      0.070      -0.000       0.004\n",
      "SP500          1.1234      0.048     23.462      0.000       1.029       1.218\n",
      "==============================================================================\n",
      "Omnibus:                       52.109   Durbin-Watson:                   1.871\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              210.791\n",
      "Skew:                           0.772   Prob(JB):                     1.69e-46\n",
      "Kurtosis:                       7.216   Cond. No.                         46.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# 增加一列全1\n",
    "X_df = sm.add_constant(x_df)\n",
    "\n",
    "model = sm.OLS(y_df, X_df)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bdf197d2-9683-4698-b63e-0478abf04b87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                 OLS Regression Results                                \n",
      "=======================================================================================\n",
      "Dep. Variable:                   AAPL   R-squared (uncentered):                   0.687\n",
      "Model:                            OLS   Adj. R-squared (uncentered):              0.686\n",
      "Method:                 Least Squares   F-statistic:                              549.2\n",
      "Date:                Thu, 23 Nov 2023   Prob (F-statistic):                    4.97e-65\n",
      "Time:                        11:10:26   Log-Likelihood:                          673.71\n",
      "No. Observations:                 251   AIC:                                     -1345.\n",
      "Df Residuals:                     250   BIC:                                     -1342.\n",
      "Df Model:                           1                                                  \n",
      "Covariance Type:            nonrobust                                                  \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "SP500          1.1265      0.048     23.434      0.000       1.032       1.221\n",
      "==============================================================================\n",
      "Omnibus:                       52.047   Durbin-Watson:                   1.846\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              210.241\n",
      "Skew:                           0.771   Prob(JB):                     2.22e-46\n",
      "Kurtosis:                       7.210   Cond. No.                         1.00\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
      "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# 无截距一元线性回归\n",
    "model_no_intercept = sm.OLS(y_df, x_df)\n",
    "results_no_intercept = model_no_intercept.fit()\n",
    "print(results_no_intercept.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1a8a7a6-594b-4630-8360-45b529a37f2a",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "432f9d67-3580-4242-a1d1-ac3071c12c2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = model.fit().params\n",
    "\n",
    "# generate x-values for  regression line\n",
    "x = np.linspace(x_df.min(),x_df.max(),10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9b921a53-e4ca-4c90-971c-89906bc7926a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    0.001893\n",
       "SP500    1.123350\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dbeaf255-a9e6-4751-9bc7-5a548881b32c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.15, 0.15)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# scatter-plot data\n",
    "plt.scatter(x_df, y_df, alpha = 0.5)\n",
    "\n",
    "plt.plot(x, p.const + p.SP500 * x,color = 'r')\n",
    "\n",
    "plt.axhline(y=0, color='k', linestyle='--')\n",
    "plt.axvline(x=0, color='k', linestyle='--')\n",
    "plt.axis('scaled')\n",
    "plt.ylabel('AAPL daily log return')\n",
    "plt.xlabel('S&P 500 daily log return, market')\n",
    "plt.xlim([-0.15,0.15])\n",
    "plt.ylim([-0.15,0.15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9710040f-9dec-4908-be35-9baba2a9dd06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x241b5cce830>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(x=x_df['SP500'], y=y_df['AAPL'], kind=\"reg\",\n",
    "              xlim = [-0.15,0.15],ylim = [-0.15,0.15])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
